This invention relates to sampled data signal analysis and in particular to methods and apparatus for sampling and reconstructing the wave shape of substantially nontransient data wherein processing of samples of signals occurs at a rate substantially less than the Nyquist rate of the highest frequency components of the sampled signal but higher than the Nyquist rate of the lowest frequency components. A related, but distinguishable field is that of direct measurement of signals. In that field, measurement techniques are constrained by the absolute speed limitations of the components in the system. In the present field, techniques have been developed for making measurements wherein the signal analysis components of the measurement system operate at frequencies or speeds substantially less than the frequency components of the measured signal. Such techniques are primarily employed for measurements of nontransient or slowly-changing signal components of high-frequency (e.g. microwave) steady-state signals.
In connection with the need to measure slowly-changing signal components in high-frequency, steady-state signals, such as signals above 1 GHz, there is a need to examine and record fast rise-time (or fall-time) signals. In the past, it has been necessary to provide an input signal trigger. Such a scheme may require circuitry capable of operation at speeds comparable to or better than the signal to be analyzed. Since this is not always practical, because of limitations imposed by the available analysis tools, an alternative is clearly needed to the traditional hardware-triggered sampling data capture system.
More specifically, what is desired is an ability to record for analysis fast rise-time signals with a conventional signal digitizer (which operates at a substantially lower speed than the signal to be analyzed). For example, a 20 million sample per second digitizer sampling a signal with 20 GHz components implies analysis by circuit components operating at 20 MHz upon a 1/1000th harmonic with a best resolution of 50 nanoseconds between each sample. In theory, a signal with a 50 nanosecond-range rise time waveform could be recorded for analysis. This is an extremely difficult task with a conventional digitizer employing state-of-the-art components and circuitry. In reality, a digitizer with a resolution of 50 nanoseconds can only resolve for identification purposes a signal having frequency components with a rise time of greater than about 100 nanoseconds. At best, it is possible to determine that a signal has a rise time of 50 nanoseconds, but it is not possible to determine important characteristics, including exactly when the event started or the shape of the rising signal between samples.
Random event signals are particularly difficult to analyze. Depending on the point of random sampling, one might be able to record the occurrence of an event at a mid-point between a series of samples representing stable states of a signal. If so, one would know only that an input signal experienced a transition during an interval of somewhat less than 100 nanoseconds because the signal would require a minimum period of two samples to move between stable states. Little more would be known about the signal.
It is nevertheless desirable to be able to examine in detail an event represented by an input signal whose resolution is on the order of only twenty picoseconds.
It is believed that there is no prior art directly relevant to the present invention. However, in the past, an instrument manufactured by Hewlett-Packard Company under the model designation 54100 has used random repetitive sampling whereby triggered samples of a repetitive waveform are taken every 25 nanoseconds, and a hardware trigger interpolator is employed to determine where each sample has occurred with respect to the trigger, i.e., whether it occurred before the trigger or after the trigger and by how much before or after the trigger it occurred. Based on where it occurred with respect to the trigger, a dot or sample point representing the position of the sample in a magnitude versus time relationship is directed to an output device such as a sampling oscilloscope screen or a printer, wherein the dot is stored and/or displayed as an element of a reconstructed or synthesized waveform. Due to the inherent shortcomings on the accuracy of triggering, there is a limitation on the accuracy of such a synthesized waveform at high frequencies.